By Edward Dowling
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Additional info for Schaum’s Outline Introduction to Mathematical Economics
EXAMPLE 2. In the absence of a graph, limits can be found by using the rules of limits enumerated above. 2 CONTINUITY A continuous function is one which has no breaks in its curve. It can be drawn without lifting the pencil from the paper. A function f is continuous at x ϭ a if: 1. , exists, at x ϭ a 2. lim f(x) exists, and x→a 3. lim f(x) ϭ f(a) x→a 34 THE DERIVATIVE AND THE RULES OF DIFFERENTIATION [CHAP. , where their denominators equal zero. 5. EXAMPLE 3. Given that the graph of a continuous function can be sketched without ever removing pencil from paper and that an open circle means a gap in the function, it is clear that f(x) is discontinuous at x ϭ 4 in Fig.
8). 8) to eliminate PS, and solve for PJ . 14. QdS ϭ 410 Ϫ 5PS Ϫ 2PJ ϭ 410 Ϫ 5(40) Ϫ 2(75) Qds ϭ 60 ϭ QsS 2) QdJ ϭ 295 Ϫ PS Ϫ 3PJ ϭ 295 Ϫ 40 Ϫ 3(75) QdJ ϭ 30 ϭ QsJ Supply and demand conditions can also be expressed in quadratic form. 10) and the supply function 26 ECONOMIC APPLICATIONS OF GRAPHS AND EQUATIONS [CHAP. 2 Either the substitution method or the elimination method can be used, since this problem involves two equations and two unknowns. 10) is solved for P in terms of Q. 25. Since neither price nor quantity can be negative, Q ϭ 3.
8. 75Y, I ϭ I0 ϭ 50, and G ϭ G0 ϭ 25. (a) Graph the aggregate demand function and show its individual components. (b) Find the equilibrium level of income. (c) How can the aggregate demand function be graphed directly, without having to graph each of the component parts? a) See Fig. 2-8. b) Equilibrium income ϭ 400. c) To graph the aggregate demand function directly, sum up the individual components, Agg. 75Y The direct graphing of the aggregate demand function coincides exactly with the graph of the summation of the individual graphs of C, I, and G above.
Schaum’s Outline Introduction to Mathematical Economics by Edward Dowling